The End of Time: The Next Revolution in Physics

Any scientific theory must establish a postulate of psychophysical parallelism: it is necessary to say what elements of the physical theory correspond to actual conscious experience. Given our current meagre understanding of consciousness, we have considerable freedom in the choice we make. Everett exploited the linearity of quantum mechanics to make his particular choice. It leads, however, to what is now widely seen as a serious technical problem.

Right at the start, Everett stated that ‘The wave function is taken as the basic physical entity with no a priori interpretation.’ He aimed to show that the interpretation of the theory emerges from ‘an investigation of the logical structure of the theory’. This aim, coupled with his insistence that the wave function is the only thing that exists, creates the difficulty, since the logical structure of the theory is generally reckoned to be represented by Dirac’s transformation theory. According to it, any quantum state can indeed be regarded as made up of other states – branches in an Everett-type ‘many-worlds’ picture. The difficulty is that this representation is not unique. There are many different ways in which one and the same state, formed from the same two ‘observer’ and ‘object’ systems, can be represented as being made up of other states. We can, for example, use position states, but we can equally well use momentum states.

The fact is that quantum mechanics is doubly indefinite. First, if states of a definite kind are chosen, any state of a composite system is a unique sum of states of its subsystems. For position states, this is shown in Figures 40 to 43. The probability distribution is spread out over a huge range of possibilities in which one particle has one definite position and the other particle has another definite position. Positions are always paired together in this way. Everett resolved the apparent conflict between our experience of a unique world and this multiplicity of possibilities by associating a separate and autonomous experience with each. However, he did not address the second indefiniteness: the states shown as positions in Figures 40 to 43 could equally well be represented by, for example, momentum states. Then pairs of momentum states result. Depending on the representation, different sets of parallel worlds are obtained: ‘position histories’ in the one case, ‘momentum histories’ in the other. One quantum evolution yields not only many histories but also many families of different kinds of history.

It was surprisingly long before this difficulty was clearly recognized as the preferred-basis problem: a definite kind of history will be obtained only if there exists some distinguished, or preferred, choice of the basis, by which is meant the kind of states used in the representation. The preferred basis problem is the EPR paradox in a different guise. Everett may have instinctively assumed that the position basis is somehow naturally singled out, but there is little evidence in his paper to confirm this.

The first question that must be addressed is surely this: what is real? Everett took the wave function to be the only physical entity. The price for this wave-function monism is the preferred-basis problem. Because the wave functions of composite systems can be represented in so many ways, the application of Everett’s ideas to different kinds of representation suggests that one and the same wave function contains not only many histories, but also many different kinds of history. It leads to a ‘many-many-worlds’ interpretation. Some accept this, but I feel there is a more attractive alternative.

A DUALISTIC PICTURE

The purists among the quantum ‘founding fathers’, above all Dirac and Heisenberg, saw a close parallel between the representation of one and the same quantum state in many ways and the possibility of putting many different coordinate systems on one and the same space-time. In relativity, this corresponds to splitting space-time into space and time in different ways. After Einstein’s great triumph, no physicist would dream of saying that this could be done in one way only. Similarly, Dirac and Heisenberg argued, there is nothing in quantum theory to suggest that there is a preferred way to represent quantum states. However, the parallel may not be accurate.